Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

2007 ◽  
Vol 23 (4) ◽  
pp. 433-444 ◽  
Author(s):  
C. F. Lee ◽  
Y. C. Chen
Keyword(s):  
Internal State ◽  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Irreversible Thermodynamics ◽  
Damage Parameter ◽  
Fatigue Tests ◽  
Future Research ◽  
Mathematical Form ◽  
State Variables ◽  
Endochronic Theory

AbstractIn this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

A Damage Model for Nonlinear Tensile Behavior of Cortical Bone

1999 ◽  
Vol 121 (5) ◽  
pp. 533-541 ◽  
Author(s):  
M. T. Fondrk ◽  
E. H. Bahniuk ◽  
D. T. Davy
Keyword(s):  
Experimental Data ◽  
Cortical Bone ◽  
Internal State ◽  
Damage Model ◽  
Experimental Studies ◽  
Inelastic Strain ◽  
Damage Parameter ◽  
Tensile Behavior ◽  
State Variables ◽  
Bending Loading

To describe the time-dependent nonlinear tensile behavior observed in experimental studies of cortical bone, a damage model was developed using two internal state variables (ISV’s). One ISV is a damage parameter that represents the loss of stiffness. A rule for the evolution of this ISV was defined based on previously observed creep behavior. The second ISV represents the inelastic strain due to viscosity and internal friction. The model was tested by simulating experiments in tensile and bending loading. Using average values from previous creep studies for parameters in the damage evolution rule, the model tended to underestimate the maximum nonlinear strains and to overestimate the nonlinear strain accumulated after load reversal in the tensile test simulations. Varying the parameters for the individual tests produced excellent fits to the experimental data. Similarly, the model simulations of the bending tests could produce excellent fits to the experimental data. The results demonstrate that the 2-ISV model combining damage (stiffness loss) with slip and viscous behavior could capture the nonlinear tensile behavior of cortical bone in axial and bending loading.

Crack Initiation Under Low-Cycle Multiaxial Fatigue in Type 316L Stainless Steel

1983 ◽  
Vol 105 (2) ◽  
pp. 138-143 ◽  
Author(s):  
B. Jacquelin ◽  
F. Hourlier ◽  
A. Pineau
Keyword(s):  
Stainless Steel ◽  
Crack Initiation ◽  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Multiaxial Fatigue ◽  
Stage I ◽  
Type B ◽  
Strain Behavior ◽  
Number Of Cycles

Low-cycle fatigue tests corresponding to fatigue life range between 103 and 105 cycles were carried out at room temperature on one heat of 316 L austenitic stainless steel. These tests included: (i) reversed tension-compression, (ii) reversed tension-compression with a superimposed steady torque, (iii) pulsated tension-compression with a stress ratio (Rσ) such that −0.5<Rσ<0, (iv) reversed and pulsated tension-compression with a superimposed steady internal pressure. In tests (ii), the torsional ratcheting effect was measured. SEM observations were used to determine the number of cycles corresponding to Stage I crack initiation and the orientation of Stage I microcracks. It was observed that the in-depth growing Type B shear microcracks were most damaging. A simple criterion is proposed Ni=No(Δγp B)α•(σnB)β where Ni is the number of cycles to crack initiation, Δγp B is the range of plastic shear strain on Type B planes, σnB is the maximum normal stress acting on these planes, No,α and β are parameters adjusted from the Manson-Coffin law and reversed cyclic stress-strain behavior.

Comparative Study of Microstructure and High Temperature Low Cycle Fatigue Behaviour of Nickel Base Superalloys Inconel 713LC and MAR-M247

2016 ◽  
Vol 713 ◽  
pp. 86-89 ◽  
Author(s):  
Ivo Šulák ◽  
Karel Obrtlík ◽  
Ladislav Čelko
Keyword(s):  
High Temperature ◽  
Fatigue Life ◽  
Low Cycle Fatigue ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Casting Defects ◽  
Cycle Fatigue ◽  
Stress Strain Curve ◽  
Nickel Base

The present work is focused on the study of microstructure and low cycle fatigue behavior of the first generation nickel-base superalloy IN 713LC (low carbon) and its promising second generation successor MAR-M247 HIP (hot isostatic pressing) at 900 °C. Microstructure of both alloys was studied by means of scanning electron microscopy (SEM). The microstructure of both materials is characterized by dendritic grains, carbides and casting defects. Size and morphology of precipitates and casting defects were evaluated. Fractographic observations have been made with the aim to reveal the fatigue crack initiation place and relation to the casting defects and material microstructure. Low cycle fatigue tests were conducted on cylindrical specimens in symmetrical push-pull cycle under strain control with constant total strain amplitude and strain rate at 900 °C in air. Hardening/softening curves, cyclic stress-strain curve and fatigue life data of both materials were obtained. Cyclic stress-strain curve of MAR M247 is shifted approximately to 120 MPa higher stress amplitudes in comparison with IN 713LC. Significantly higher fatigue life of MAR-M247 has been observed in Basquin representation. On the other hand IN 713LC shows prolonged lifetime compared with MAR-M247 in the Coffin-Manson representation. Results obtained from high temperature low cycle fatigue tests are discussed.

Deformation Kinetics of Steady Creep in Sn/Pb Solder Alloys With Applications

2004 ◽  
Vol 20 (2) ◽  
pp. 85-93 ◽  
Author(s):  
C. F. Lee ◽  
M. K. Chang ◽  
W. K. Chung
Keyword(s):  
Constitutive Equation ◽  
Internal State ◽  
Tensile Creep ◽  
Future Research ◽  
State Variables ◽  
Steady Creep ◽  
Solder Alloys ◽  
Creep Tests ◽  
Shear Creep ◽  
Deformation Kinetics

AbstractIn this paper, a constitutive equation of steady creep rates:is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

Axial and Diametral Cyclic Stress—Strain Response in Plain and Circumferentially Notched Cylindrical Bars at 550 °C

2006 ◽  
Vol 41 (4) ◽  
pp. 265-286 ◽  
Author(s):  
R. P Skelton ◽  
G. A Webster
Keyword(s):  
Low Cycle Fatigue ◽  
Notch Root ◽  
Hysteresis Loops ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Gauge Length ◽  
Stress Strain ◽  
Deformation Response ◽  
Notched Specimens ◽  
Observed Behaviour

Cyclic stress-strain tests were undertaken at 550 °C on plain specimens and notched specimens of different notch acuities in several low- and high-alloy ferritic steels (1Cr-Mo-V, NF616, TB12M, and HCM12A). Integrated axial strains were measured between the minimum sections of the notches using a longitudinal extensometer, while surface hoop strains were measured by means of a diametral extensometer with probes located across the notch root. The same extensometry was employed in plain specimens. Over a period of 100 cycles, softening occurred in all plain specimens. These effects were also demonstrated in notched specimens in both axial and diametral directions, although to a lesser degree. From hysteresis loops determined in the notch tests, the cyclic deformation response of the notched regions was expressed in terms of an ‘equivalent gauge length’. Deviations from elastic-plastic behaviour in plain specimens were noted in that the commonly used ‘effective Poisson's ratiO' was greater than calculated. The effect was investigated further by exploring the characteristics of a very shallow notch, induced by straining a plain specimen to the onset of necking and beyond. The implications of observed behaviour in strain-control low-cycle fatigue tests is discussed.

scholarly journals Shape of the Cyclic Stress-Strain Loop in the Low-Cycle Fatigue Tests

1969 ◽  
Vol 12 (54) ◽  
pp. 1279-1284 ◽  
Author(s):  
Eiryo SHIRATORI ◽  
Yoichi OBATAYA
Keyword(s):  
Low Cycle Fatigue ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Cycle Fatigue ◽  
Stress Strain

Cyclic Deformation of a Modern TiAl Alloy at High Temperatures

2014 ◽  
Vol 891-892 ◽  
pp. 1131-1136 ◽  
Author(s):  
Tomáš Kruml ◽  
Alice Chlupová ◽  
Karel Obrtlík
Keyword(s):  
Lamellar Structure ◽  
Tial Alloy ◽  
Low Cycle Fatigue ◽  
Lamellar Microstructure ◽  
Strain Curve ◽  
Cyclic Stress ◽  
Cyclic Softening ◽  
Fatigue Tests ◽  
Tensile Curve ◽  
Cyclic Straining

Ternary TiAl alloy with 8 at.% Nb and lamellar microstructure is subjected to low cycle fatigue tests at temperatures ranging from room temperature to 800 °C. The aim of the study is to find limit conditions when the microstructure is still stable and to study mechanisms of microstructural degradation when this limit is exceeded. Up to 750 °C, no cyclic softening or hardening is observed and cyclic stress-strain curve follows the tensile curve. Cyclic softening is characteristic for 800 °C. The TEM observation did not reveal any substantial changes in the microstructure due to the cycling up to 700°C. The lamellar structure is altered by cyclic straining at 750 °C and, to a higher extent, at 800°C. In specimens cycled to fracture at 800 °C, the domains without lamellar structure cover about 10% of volume and are almost dislocation free. The destruction of lamellar microstructure is the reason for the marked cyclic softening at 800 °C.

Low Cycle Fatigue Behaviors of TI-6AL-4V Alloy Controlled by Strain and Stress

2012 ◽  
Vol 525-526 ◽  
pp. 441-444
Author(s):  
Rui Feng Wang ◽  
You Tang Li ◽  
Hu Ping An
Keyword(s):  
Stress Ratio ◽  
Low Cycle Fatigue ◽  
Cyclic Strain ◽  
Cyclic Creep ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Cycle Fatigue ◽  
Compressive Stresses ◽  
Initial Stage ◽  
Main Factor

The low cycle fatigue behaviors of TI-6AL-4V alloy controlled by strain were investigated by experiment. The fatigue tests were performed at room temperature, and cyclic strain and stress ratio are 0.1 with triangle load wave. The results show that TI-6AL-4V alloy is soften rapidly under the cyclic tensile stresses and it is harden rapidly under the cyclic compressive stresses during the initial-stage of strain controlled fatigue, and the rates of cyclic soften and cyclic harden are decreased with the fatigue progress. The soften rate is related to the cyclic strain but little to the cyclic stress during the overall fatigue progress. The change of cyclic stress is related to the macro friction stresses. The results of experiment show that obvious cyclic creep occurs under the stress controlled low cycle fatigue conditions, and the magnitude of cyclic creep strain is related to the maximum cyclic stress. The softening of tensile friction stresses is the main factor of cyclic creep.

Investigation on Fatigue Properties of Cold Stretched Austenitic Stainless Steel

2011 ◽  
Author(s):  
Cunjian Miao ◽  
Jinyang Zheng ◽  
Li Ma ◽  
Duyi Ye
Keyword(s):  
Stainless Steel ◽  
Austenitic Stainless Steel ◽  
Design Method ◽  
Low Cycle Fatigue ◽  
Rolling Direction ◽  
Cyclic Stress ◽  
Fatigue Tests ◽  
Pressure Vessels ◽  
Fatigue Properties ◽  
Fatigue Design

Cold stretched pressure vessels from austenitic stainless steel (ASS), which are sometimes subjected to alternative loads during operation, have been widely used for storage and transportation of liquefied gases. Understanding how the fatigue properties respond to cold stretching is the basis for establishing fatigue design method of such vessels. This paper involves in the fatigue properties of ASS with 9% plastic deformation by pre-stretching parallel to the rolling direction at room temperature. For this purpose, low-cycle fatigue tests at total strain amplitudes ranging from ±0.4 to 0.8% of cold stretched ASS EN 1.4301 (equivalents include UNS S30400, AISI 304) are performed, while the martensite contents are measured during the fatigue cycles. A comparison study of cyclic stress-strain behavior and fatigue lives is carried out for both cold stretched and solution annealed specimens. Based on the testing results, a S-N curve of cold stretched ASS is obtained, which is compared with the design curves given by the standards such as ASME BPVC VIII-2. These works may help to establish a favorable foundation for the development of fatigue design in cold stretched pressure vessel.

Cyclic Softening of Cu-Ni-Si Alloy Single Crystals under Low-Cycle Fatigue

2010 ◽  
Vol 654-656 ◽  
pp. 1287-1290 ◽  
Author(s):  
Toshiyuki Fujii ◽  
Hiroshi Kamio ◽  
Yoshifumi Sugisawa ◽  
Susumu Onaka ◽  
Masaharu Kato
Keyword(s):  
Plastic Strain ◽  
Single Crystals ◽  
Low Cycle Fatigue ◽  
Strain Curve ◽  
Electron Microscopic Observation ◽  
Cyclic Hardening ◽  
Cyclic Stress ◽  
Cyclic Softening ◽  
Fatigue Tests ◽  
Electron Microscopic

Cu-2.2wt%Ni-0.5wt%Si alloy single crystals were grown by the Bridgman method and aged at 723 K for 10 h to form Ni2Si precipitates. Fully reversed tension-compression fatigue tests were conducted on the aged single crystals with a single slip orientation under constant plastic-strain amplitudes at room temperature. Cyclic softening occurred at plastic-strain amplitudes between 2.5x10-4 and 2.5x10-2. Using the maximum stress amplitude in each cyclic hardening/softening curve, a pseudo cyclic stress-strain curve (CSSC) was obtained. The CSSC was found to exhibit a plateau region with a stress level of about 167 MPa. Transmission electron microscopic observation revealed the formation of persistent slip bands (PSBs) in the plateau regime. It was found that the Ni2Si precipitate particles were intensively sheared by glide dislocations within the PSBs and were eventually re-dissolved into the Cu matrix. The macroscopic cyclic softening can be attributed to the local softening induced by the re-dissolution of the Ni2Si particles in the PSBs.

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